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Let's solve the given problem step-by-step.

### Given:
\[
\frac{3}{a} - \frac{2}{b} = 4
\]
\[
\frac{1}{a} + \frac{1}{b} = 3
\]
We need to find the value of \(\frac{a}{b}\).

### Step 1: Solve the given equations
Let’s first rewrite the given equations for clarity:

1. \(\frac{3}{a} - \frac{2}{b} = 4\)
2. \(\frac{1}{a} + \frac{1}{b} = 3\)

### Step 2: Let \(x = \frac{1}{a}\) and \(y = \frac{1}{b}\)
Substituting, the equations become:
\[
3x - 2y = 4
\]
\[
x + y = 3
\]

### Step 3: Solve this system of linear equations
From the second equation:
\[
y = 3 - x
\]
Substituting \(y\) in the first equation:
\[
3x - 2(3 - x) = 4
\]
\[
3x - 6 + 2x = 4
\]
\[
5x - 6 = 4
\]
\[
5x = 10
\]
\[
x = 2
\]

Substituting \(x = 2\) back into \(y = 3 - x\):
\[
y = 3 - 2 = 1
\]

### Step 4: Find \(\frac{a}{b}\)
Recall that \(x = \frac{1}{a}\) and \(y = \frac{1}{b}\). Therefore:
\[
a = \frac{1}{x} = \frac{1}{2}, \quad b = \frac{1}{y} = 1
\]
Hence,
\[
\frac{a}{b} = \frac{\frac{1}{2}}{1} = \frac{1}{2}
\]

The correct answer is (C) \(\frac{1}{2}\).

Would you like a more detailed explanation or have any questions?

### Here are 5 related questions:
1. How do you solve simultaneous linear equations using substitution or elimination methods?
2. What are the common strategies for solving fractional equations?
3. How can you check if your solution to a system of equations is correct?
4. How does the substitution method compare to other methods for solving systems of equations?
5. What real-world situations can be modeled using systems of linear equations?

**Tip:** When dealing with fractions in equations, substituting variables for complex expressions can simplify the problem.

a ve b sıfırdan farklı gerçek sayılardır.
\(\frac{3}{a} - \frac{2}{b} = 4\) ve \(\frac{1}{a} + \frac{1}{b} = 3\) olduğuna göre \(\frac{a}{b}\) kaçtır?

Learn how to solve a fractional system of equations where \(\frac{3}{a} - \frac{2}{b} = 4\) and \(\frac{1}{a} + \frac{1}{b} = 3\), to find \(\frac{a}{b}\). Suitable for Grade 10 students, covering substitution methods and solving linear systems.

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